Global stability of an SI epidemic model with feedback controls in a patchy environment

Hong Li Li; Long Zhang; Zhidong Teng; Yao Lin Jiang; Ahmadjan Muhammadhaji

doi:10.1016/j.amc.2017.10.057

Global stability of an SI epidemic model with feedback controls in a patchy environment

Hong Li Li
, Long Zhang
, Zhidong Teng
, Yao Lin Jiang
, Ahmadjan Muhammadhaji

School of Mathematics and Statistics

Xinjiang University

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

In this paper, we investigate an SI epidemic model with feedback controls in a patchy environment where individuals in each patch can disperse among n(n ≥ 2) patches. We derive the basic reproduction number R₀ and prove that the disease-free equilibrium is globally asymptotically stable if R₀ ≤ 1. In the case of R₀ > 1, we derive sufficient conditions under which the endemic equilibrium is unique and globally asymptotically stable. Our proof of global stability utilizes the method of global Lyapunov functions and results from graph theory. Numerical simulations are carried out to support our theoretical results.

Original language	English
Pages (from-to)	1339-1351
Number of pages	13
Journal	Applied Mathematics and Computation
Volume	321
DOIs	https://doi.org/10.1016/j.amc.2017.10.057
State	Published - 15 Mar 2018

Keywords

Basic reproduction number
Feedback controls
Global stability
Lyapunov function
Patchy environment
SI epidemic model

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10.1016/j.amc.2017.10.057

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title = "Global stability of an SI epidemic model with feedback controls in a patchy environment",

abstract = "In this paper, we investigate an SI epidemic model with feedback controls in a patchy environment where individuals in each patch can disperse among n(n ≥ 2) patches. We derive the basic reproduction number R0 and prove that the disease-free equilibrium is globally asymptotically stable if R0 ≤ 1. In the case of R0 > 1, we derive sufficient conditions under which the endemic equilibrium is unique and globally asymptotically stable. Our proof of global stability utilizes the method of global Lyapunov functions and results from graph theory. Numerical simulations are carried out to support our theoretical results.",

keywords = "Basic reproduction number, Feedback controls, Global stability, Lyapunov function, Patchy environment, SI epidemic model",

author = "Li, \{Hong Li\} and Long Zhang and Zhidong Teng and Jiang, \{Yao Lin\} and Ahmadjan Muhammadhaji",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2018",

month = mar,

day = "15",

doi = "10.1016/j.amc.2017.10.057",

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T1 - Global stability of an SI epidemic model with feedback controls in a patchy environment

AU - Li, Hong Li

AU - Zhang, Long

AU - Teng, Zhidong

AU - Jiang, Yao Lin

AU - Muhammadhaji, Ahmadjan

PY - 2018/3/15

Y1 - 2018/3/15

N2 - In this paper, we investigate an SI epidemic model with feedback controls in a patchy environment where individuals in each patch can disperse among n(n ≥ 2) patches. We derive the basic reproduction number R0 and prove that the disease-free equilibrium is globally asymptotically stable if R0 ≤ 1. In the case of R0 > 1, we derive sufficient conditions under which the endemic equilibrium is unique and globally asymptotically stable. Our proof of global stability utilizes the method of global Lyapunov functions and results from graph theory. Numerical simulations are carried out to support our theoretical results.

AB - In this paper, we investigate an SI epidemic model with feedback controls in a patchy environment where individuals in each patch can disperse among n(n ≥ 2) patches. We derive the basic reproduction number R0 and prove that the disease-free equilibrium is globally asymptotically stable if R0 ≤ 1. In the case of R0 > 1, we derive sufficient conditions under which the endemic equilibrium is unique and globally asymptotically stable. Our proof of global stability utilizes the method of global Lyapunov functions and results from graph theory. Numerical simulations are carried out to support our theoretical results.

KW - Basic reproduction number

KW - Feedback controls

KW - Global stability

KW - Lyapunov function

KW - Patchy environment

KW - SI epidemic model

UR - https://www.scopus.com/pages/publications/85034100864

U2 - 10.1016/j.amc.2017.10.057

DO - 10.1016/j.amc.2017.10.057

M3 - 文章

AN - SCOPUS:85034100864

SN - 0096-3003

VL - 321

SP - 1339

EP - 1351

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Global stability of an SI epidemic model with feedback controls in a patchy environment

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Keywords

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